TY - JOUR

T1 - Relativistic charge currents in oblique electric and magnetic fields

AU - Melia, Fulvio

AU - Fatuzzo, Marco

N1 - Funding Information:
This research was supported in part by NSF Grant PHY 88-57218, NASA Grant NAGW-1609 and the Alfred P. Sloan Foundation. Most of the numerical calculations were carried out at the National Center for Supercomputing Applications in Urbana-Champaign. M. F. is a Northwestern University Fellow. F. M. is a Presidential Young Investigator and an Alfred P. Sloan Fellow.

PY - 1991

Y1 - 1991

N2 - Runaway processes on neutron stars leading to the sudden release of large quantities of energy (up to of order 1040 erg) on time scales as short as a fraction of a second involve plasma heating and particle acceleration in superstrong magnetic fields H (of order 1012 G). These transient events are interesting from a theoretical standpoint because they require knowledge of particle transport properties in low-density plasmas (ne ≲ 1025cm−3) threaded by both electric (E) and magnetic fields. The evaluation of matrix elements involving solutions to the Dirac equation for such a field configuration is often difficult and sometimes impossible, since no completely normalized wave function has yet been found. Here it is shown that, in the special case of E/H ≲ 10−4, a simplification of the overlap integrals permits an analytical integration that yields explicit expressions for the relativistic charge currents needed in the computation of the anisotropic conductivity tensor when E.H ≠ 0. The application of these results to the evaluation of the conductivity is briefly discussed. Among other things, this work is relevant to a theory of resistive magnetic tearing instabilities in a quantizing field.

AB - Runaway processes on neutron stars leading to the sudden release of large quantities of energy (up to of order 1040 erg) on time scales as short as a fraction of a second involve plasma heating and particle acceleration in superstrong magnetic fields H (of order 1012 G). These transient events are interesting from a theoretical standpoint because they require knowledge of particle transport properties in low-density plasmas (ne ≲ 1025cm−3) threaded by both electric (E) and magnetic fields. The evaluation of matrix elements involving solutions to the Dirac equation for such a field configuration is often difficult and sometimes impossible, since no completely normalized wave function has yet been found. Here it is shown that, in the special case of E/H ≲ 10−4, a simplification of the overlap integrals permits an analytical integration that yields explicit expressions for the relativistic charge currents needed in the computation of the anisotropic conductivity tensor when E.H ≠ 0. The application of these results to the evaluation of the conductivity is briefly discussed. Among other things, this work is relevant to a theory of resistive magnetic tearing instabilities in a quantizing field.

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U2 - 10.1017/S0022377800015816

DO - 10.1017/S0022377800015816

M3 - Article

AN - SCOPUS:0026171471

SN - 0022-3778

VL - 45

SP - 415

EP - 425

JO - Journal of Plasma Physics

JF - Journal of Plasma Physics

IS - 3

ER -